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Solve the following :

Question:

In a gamma decay process, the initial energy of a nucleus of mass $M$ decreases, a gamma photon of energy $\mathrm{E}$ and linear momentum $\mathrm{E} / \mathrm{c}$ is emitted and the nucleus recoils. Find the decrease in internal energy.

Solution:

K.E. of nucleus $=\frac{p N^{2}}{2 M_{N}}=\frac{E^{2}}{2 M_{N} c^{2}}$

Decrease in internal energy

$E_{\text {int }(N)}-E_{\text {int }\left(N^{\prime}\right)}=E_{r}+K \cdot E$

$=E+\frac{E^{2}}{2 M_{N} c^{2}}$

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